Problem: Express your answer as a mixed number simplified to lowest terms. $13\dfrac{1}{17}-5\dfrac{2}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {13\dfrac{3}{51}}-{5\dfrac{34}{51}}$ Convert ${13\dfrac{3}{51}}$ to ${12 + \dfrac{51}{51} + \dfrac{3}{51}}$ So the problem becomes: ${12\dfrac{54}{51}}-{5\dfrac{34}{51}}$ Separate the whole numbers from the fractional parts: $= {12} + {\dfrac{54}{51}} - {5} - {\dfrac{34}{51}}$ Bring the whole numbers together and the fractions together: $= {12} - {5} + {\dfrac{54}{51}} - {\dfrac{34}{51}}$ Subtract the whole numbers: $=7 + {\dfrac{54}{51}} - {\dfrac{34}{51}}$ Subtract the fractions: $= 7+\dfrac{20}{51}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{20}{51}$